Semantics

Semiotics is the study of signs. It is an interdisciplinary field that examines what signs are, how they form sign systems, and how individuals use them to communicate meaning. Its main branches are syntactics, which addresses formal relations between signs, semantics, which addresses the relation between signs and their meanings, and pragmatics, which addresses the relation between signs and their users. Semiotics is related to linguistics but has a broader scope that includes nonlinguistic signs, such as maps and clothing.

Signs are entities that stand for something else, like the word cat, which stands for a carnivorous mammal. They can take many forms, such as sounds, images, written marks, and gestures. Iconic signs operate through similarity. For them, the sign vehicle resembles the referent, such as a portrait of a person. Indexical signs are based on a direct physical link, such as smoke as a sign of fire. For symbolic signs, the relation between sign vehicle and referent is conventional or arbitrary, which applies to most linguistic signs. Models of signs analyze the basic components of signs. Ferdinand de Saussure's dyadic model identifies a perceptible image and a concept as the core elements, whereas Charles Sanders Peirce's triadic model distinguishes a sign vehicle, a referent, and an effect in the interpreter's mind.

In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings (alphanumeric sequences of symbols, usually as equations) using established manipulation rules. A central idea of formalism "is that mathematics is not a body of propositions representing an abstract sector of reality, but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess."

According to formalism, mathematical statements are not "about" numbers, sets, triangles, or any other mathematical objects in the way that physical statements are about material objects. Instead, they are purely syntactic expressions—formal strings of symbols manipulated according to explicit rules without inherent meaning. These symbolic expressions only acquire interpretation (or semantics) when we choose to assign it, similar to how chess pieces follow movement rules without representing real-world entities. This view stands in stark contrast to mathematical realism, which holds that mathematical objects genuinely exist in some abstract realm.

Saul Aaron Kripke (/ˈkrɪpki/; November 13, 1940 – September 15, 2022) was an American analytic philosopher and logician. He was Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emeritus professor at Princeton University. From the 1960s until his death, he was a central figure in a number of fields related to mathematical and modal logic, philosophy of language and mathematics, metaphysics, epistemology, and recursion theory.

Kripke made influential and original contributions to logic, especially modal logic. His principal contribution is a semantics for modal logic involving possible worlds, now called Kripke semantics. He received the 2001 Schock Prize in Logic and Philosophy.

In logic, the logical form of a statement is a precisely specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system. In an ideal formal language, the meaning of a logical form can be determined unambiguously from syntax alone. Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language.

The logical form of an argument is called the argument form of the argument.

The analytic–synthetic distinction is a semantic distinction used primarily in philosophy to distinguish between propositions (in particular, statements that are affirmative subject–predicate judgments) that are of two types: analytic propositions and synthetic propositions. Analytic propositions are true or not true solely by virtue of their meaning, whereas synthetic propositions' truth, if any, derives from how their meaning relates to the world.

While the distinction was first proposed by Immanuel Kant, it was revised considerably over time, and different philosophers have used the terms in very different ways. Furthermore, some philosophers (starting with Willard Van Orman Quine) have questioned whether there is even a clear distinction to be made between propositions which are analytically true and propositions which are synthetically true. Debates regarding the nature and usefulness of the distinction continue to this day in contemporary philosophy of language.

Colorless green ideas sleep furiously was composed by Noam Chomsky in his 1957 book Syntactic Structures as an example of a sentence that is grammatically well-formed, but semantically nonsensical. The sentence was originally used in his 1955 thesis The Logical Structure of Linguistic Theory and in his 1956 paper "Three Models for the Description of Language". There is no obvious understandable meaning that can be derived from it, which demonstrates the distinction between syntax and semantics, and the idea that a syntactically well-formed sentence is not guaranteed to also be semantically well-formed. As an example of a category mistake, it was intended to show the inadequacy of certain probabilistic models of grammar, and the need for more structured models.

A formal grammar is a set of symbols and the production rules for rewriting some of them into every possible string of a formal language over an alphabet. A grammar does not describe the meaning of the strings — only their form.

In applied mathematics, formal language theory is the discipline that studies formal grammars and languages. Its applications are found in theoretical computer science, theoretical linguistics, formal semantics, mathematical logic, and other areas.

In Islamic philosophy, Sufi metaphysics is centered on the concept of وحدة, waḥdah, 'unity' or توحيد, tawhid. Two main Sufi philosophies prevail on this topic. Wahdat al-wujūd literally means "the Unity of Existence" or "the Unity of Being." Wujūd, meaning "existence" or "presence", here refers to God. On the other hand, waḥdat al-shuhūd, meaning "Apparentism" or "Monotheism of Witness", holds that God and his creation are entirely separate.

Some scholars have claimed that the difference between the two philosophies differ only in semantics and that the entire debate is merely a collection of "verbal controversies" which have come about because of ambiguous language. However, the concept of the relationship between God and the universe is still actively debated both among Sufis and between Sufis and non-Sufi Muslims.

Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joyal. It was first conceived for modal logics, and later adapted to intuitionistic logic and other non-classical systems. The development of Kripke semantics was a breakthrough in the theory of non-classical logics, because the model theory of such logics was almost non-existent before Kripke (algebraic semantics existed, but were considered 'syntax in disguise').

Communication is commonly defined as the transmission of information. Its precise definition is disputed and there are disagreements about whether unintentional or failed transmissions are included and whether communication not only transmits meaning but also creates it. Models of communication are simplified overviews of its main components and their interactions. Many models include the idea that a source uses a coding system to express information in the form of a message. The message is sent through a channel to a receiver who has to decode it to understand it. The main field of inquiry investigating communication is called communication studies.

A common way to classify communication is by whether information is exchanged between humans, members of other species, or non-living entities such as computers. For human communication, a central contrast is between verbal and non-verbal communication. Verbal communication involves the exchange of messages in linguistic form, including spoken and written messages as well as sign language. Non-verbal communication happens without the use of a linguistic system, for example, using body language, touch, and facial expressions. Another distinction is between interpersonal communication, which happens between distinct persons, and intrapersonal communication, which is communication with oneself. Communicative competence is the ability to communicate well and applies to the skills of formulating messages and understanding them.